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Divided By Zero

By Cosmic Cairns on February 5, 2026 11:40 pm

I always remember being fascinated in math class when the teachers told us you weren't allowed to divide numbers by zero. And if you asked why not, they never seemed to have a good explanation.  You just can't.  Tell me not to do something and of course it immediately becomes more interesting.  I remember the old school calculators would give you some kind of error and I just tried it right now on my phone calculator and it flat out says "can't divide by zero."  It's like you've stumbled into some place where ordinary math breaks. 

_______________________________________________________________________________________________________________

I try to wrap my head around
And I wonder why the cold wind blows
And the river flows to the sea

Numbers divided by zero
Don't exist but if it's all the same
Utter nonsense reigns it seems to me

And all the digits start to
Bend break form fractured fractions
And reverse course alter direction
And invert change turn themselves inside out
And flip flop fumble turn upside down
And roll shake tremble and rattle
All around space time and dimensions
Still unknown and leaves my mind blown
Now watch it go go go go go go go go...

I want to try to understand
Why the clouds above me shift and change
Always rearrange what they are

Something essential seems to be
There but constantly just out of reach
Circling the breach near and far

Divided by zero
And I can feel the fear go
Divided by zero
Now sit and watch the tears roll down

Audio works licensed by author under:
Copyright All rights reserved

I really like you usage of accoustic gutiar pumping the rhythm away. It brings a folk vibe to this space odyssey. (i think the 70s synth hits take me to the space odysseys).
Great guitars, and i like the subtle lines you play under the singing.

So much positive energy! That build up with the gogogogo is so fun.

If you divide by zero then you risk resetting the universe to the time of the singularity. This is bad. Like "crossing the streams" bad.

me stimming in my kitchen for the next week:
"And all the digits start to
Bend!
Break!
Form Fractured Fractions!

I love the really heavy distortion on the opening and the bridge. Also...

As a hardcore math nerd... I think the above does a pretty good job of explaining why one "cant" divide by zero... and I have a whole soapbox on how math education is... just... generally bad, so encountering teachers who say things like "you just can't" is really just a bad look for those math teachers (like they probably should have paid closer attention in Abstract Algebra).  But, I think "cant divide by zero", isn't really the right way to state that.  There are plenty of algebras where you can/could divide by zero, they just aren't useful to humans doin' normal human things.  It's more that there is no way to define zero (and infinity), such that dividing by it is useful while maintaining all the other things we expect from "normal" maths. 

So like zero is useful because it represents the absence of things right? If I have zero pizza that is less than one pizza or a half, or any quantity of pizza.  That's a useful thing to be able to represent.  But, if you think about what division (most commonly) is used to describe, it's taking something and splitting it equally in to parts. So if I have 1 pizza and I want to divide that amongst 4 people, than I can conceptualize how much pizza each person will get, like I can imagine how big that slice of pizza is... but if I have one pizza and I want to divide that into 0 parts, the very concept is incoherent... like the smallest (useful) number of parts I can divide a thing up into is 1... then it becomes whole...  Zero is just not useful in that context.  It does open a can of worms because "what about 0.25?"... and there are a number of more abstract mathematical constructs for division, but the above video hits the high points for that stuff.  Really it's just that in "normal" maths, if we construct a definition for zero, while also defining what it means to divide by it, then we end up needing 1 to equal 2, or everything has to equal zero for it to work... so we just leave X/0 as "undefined" because defining that point forces a bunch of other things to either be useless or nonsense.

So... not that you asked... but there you go.

speaking of E6, did Robert record you doing that fuzzed out acoustic? so tasty!

love the melodie on this, Cosmic! a kaleidoscopic drive through the math forest!

maybe we can't divide by zero, but can we...

It is crazy how clean and catchy this song is. Kinda reminds me of 90s/early 2000s rock like Barenaked Ladies or They Might Be Giants. Huge fan of the Monotron Delay kicking in for flavor as well

woot! those guitars get the fun groove going right away.  Catchy vocal harmonies and love how it goes into the mellotronny section where it takes off with the distortion.  Well done!

Great inspiration for a song! Great guitars, and whatever that wobbly high pitched thing is at the end lol! Great work.

oh you got me math, we don't explain anything anymore, the younger kids are soon to be left with, well that's what the AI Oracle said the answer, all must bend to its wisdom (because we don't have any anymore)

I tried dividing by zero today and the world didn't end!

That fuzzed out acoustic was unexpected and put a huge smile on my face. Lyrics are amazing as always. This is really excellent.

oh hell yeah this thing moves. Nice guitar work! Doubled vocals++++ 1:30 love the rhythmic lyric delivery. This is such a solid song!

Absolutely love the bit at 2:41 omg

EPIC vibes of INFINITE OMNIPOTENCE! It's as if, in thinking about how your math teacher said you "can't" do something, the spirit of the song is yelling out, "WE CAN DO ANYTHING!!" I love how you can take anything to this huge level of open-hearted positivity in your songs. I like the repeated lyrical motif at the end, too, taking it into a slightly different feel but still on the same level of 'YES I CAN!' while we roll out into the sunset heart

also, as for the math of 'dividing by zero', the word "can't" doesn't seem right since it was phrased like a 'rule', so i see your instinct is correct: if math is like science, these aren't 'rules' but more like 'descriptions/symbols' of 'nature'. my math teacher in elementary school didn't really phrase it like that(because i was in a classroom where we would've just kept asking "but why not?" if they did...) so i remember my math teacher specifically saying, "zero is the same as dividing by nothing, and if you divide by nothing, then it's as if you never divided anything, but instead multiplied it by infinity..." then they proceeded to show on a calculator how if you divide by numbers between 1 and 0, and get infinitessimally smaller, the result gets infinitely bigger (try dividing any number by 0.01 on a calculator, then try dividing that same number by 0.0000001 on the calculator, the result keeps getting larger)... which is interesting, when i hear your song here, the feel of it from beginning to end, gets infinitely bigger as we come to this point where you "divided by zero, now sit and watch the tears roll down", you come to that infinitely large feeling of an infinitely opened heart!! just saying, i see what ya did there wink heart

I love the sound and upbeat mood. My all-time favourite music genre is powerpop and I'd classify this not only as part of that genre but a solid representation that I will absolutely add to my summer playlist.

Side note: I appreciate the Monotron love

I can hear the smile on your face as you were singing the lyrics to this song. What a blast! Loved what you did with the doubling there, too. Everything just works in this song! Thank you for producing it. heart

A new spin on "math rock" tongue  Your vocals on this track remind me of The Shins!

Napear wrote:

As a hardcore math nerd...


This was a great discussion, thanks!

Napear wrote:

There are plenty of algebras where you can/could divide by zero, they just aren't useful to humans doin' normal human things


There are... plenty of algebras?  (For non-humans?  Or possibly humans doing non-normal human things?)

ineff wrote:

There are... plenty of algebras?  (For non-humans?  Or possibly humans doing non-normal human things?)

lol… yeah, an algebra is a vector space equipped with a bilinear product… which is just fancy nerd speak that means you have a collection of items (the vector space) and a specific, predictable way to mash them together (bilinear product).  And, there are loads of them… the thing most people study in high school (or whatever) is Finite-Dimensional Associative Commutative Real Division Algebra… which is a shit ton of nonsense words for most people, hence just “Algebra”.  And, yeah all the algebras where one can divide by zero fall into the humans doing non-normal human things like constructing Riemann spheres and the like… though I suppose there is an argument that physicist and mathematicians could fall into the non-human category… so o guess read that either way ꉂ (´∀`)ʱªʱªʱª

A strong turn of the millennium punk-rock-pop vibe that I haven't heard in a minute. Fun though! The synth/self-oscillating delay towards the end is wild. Cool little tune!

Another sweet bit of power-pop, with a bright melody and vocal harmonies yes, but also some cool weirdness. Love the sneaky 6 -> 4 transitions from the mellotron-y sections to the main song. The peaky monotron sweep transitions are wild. And I love the tone in the guitar solo. Go! (go go go go go go go...)

I was thinking Built to Spill right when I saw the title too like @jwh

This is great, the guitar is so crunchy and the sweepy lead thing is sweet. Love the bridge at 2:40 too, nice contrast.

Hey, great song. Vocals sounds great, love the lyrics. Acoustic sounds perfect for it. Came for the song, stayed for the math talk. It is interesting stuff that dividing by zero. I'm not sure I fully get it, and not sure I'll put my brain energy there now. Will probably check out the video Napear shared though. Smarter every day. Good song!

Good energy in this bop.
I think you've been told enough why you can't, it depends on the field really.
- Leega

Went back to high school maths class with this one! Such a great bop, gonna be in my head all week. Kinda' gave me cosy but thoughtful TMBG vibes, which I what I used to listen to when I was meant to be doing maths homework

heart

Kedbreak136 wrote:

I really like you usage of accoustic gutiar pumping the rhythm away. It brings a folk vibe to this space odyssey. (i think the 70s synth hits take me to the space odysseys).
Great guitars, and i like the subtle lines you play under the singing.

So much positive energy! That build up with the gogogogo is so fun.

If you divide by zero then you risk resetting the universe to the time of the singularity. This is bad. Like "crossing the streams" bad.

Thanks!  I think folky space odyssey is an appropriate description.  And yeah, never cross the streams!



bc likes you wrote:

me stimming in my kitchen for the next week:
"And all the digits start to
Bend!
Break!
Form Fractured Fractions!

I hope it made your kitchen time fun this week and didn't become one of those annoying sorts of earworms.  smile  Thanks for listening!



Napear wrote:

I love the really heavy distortion on the opening and the bridge. Also...

As a hardcore math nerd... I think the above does a pretty good job of explaining why one "cant" divide by zero... and I have a whole soapbox on how math education is... just... generally bad, so encountering teachers who say things like "you just can't" is really just a bad look for those math teachers (like they probably should have paid closer attention in Abstract Algebra).  But, I think "cant divide by zero", isn't really the right way to state that.  There are plenty of algebras where you can/could divide by zero, they just aren't useful to humans doin' normal human things.  It's more that there is no way to define zero (and infinity), such that dividing by it is useful while maintaining all the other things we expect from "normal" maths. 

So like zero is useful because it represents the absence of things right? If I have zero pizza that is less than one pizza or a half, or any quantity of pizza.  That's a useful thing to be able to represent.  But, if you think about what division (most commonly) is used to describe, it's taking something and splitting it equally in to parts. So if I have 1 pizza and I want to divide that amongst 4 people, than I can conceptualize how much pizza each person will get, like I can imagine how big that slice of pizza is... but if I have one pizza and I want to divide that into 0 parts, the very concept is incoherent... like the smallest (useful) number of parts I can divide a thing up into is 1... then it becomes whole...  Zero is just not useful in that context.  It does open a can of worms because "what about 0.25?"... and there are a number of more abstract mathematical constructs for division, but the above video hits the high points for that stuff.  Really it's just that in "normal" maths, if we construct a definition for zero, while also defining what it means to divide by it, then we end up needing 1 to equal 2, or everything has to equal zero for it to work... so we just leave X/0 as "undefined" because defining that point forces a bunch of other things to either be useless or nonsense.

So... not that you asked... but there you go.

  Thanks for the indepth comment and I liked the video a lot actually.  I may not have asked, but I did say I find it fascinating.  One of my best friends in college was a math major and we had some interesting conversations along these lines sometimes, although sometimes he went beyond my comprehension.  smile  I was an English major so my mind works more naturally with words than numbers or symbols.  I did get satisfaction back in the day from successfully completing a calculus problem, and I was able to do it, but it took a bit of mental effort for me for sure.  And yes, education in the U.S. is often pretty bad.  I had some good math teachers along the way, and a few terrible ones.  Not surprisingly I did much better in the classes with the better teachers.



jwh wrote:

speaking of E6, did Robert record you doing that fuzzed out acoustic? so tasty!

love the melodie on this, Cosmic! a kaleidoscopic drive through the math forest!

maybe we can't divide by zero, but can we...

Gotta love some fuzzy distorted acoustics.  And that Built to Spill song is a classic.  Perhaps a spiritual ancestor to this one?



Earp Lug wrote:

It is crazy how clean and catchy this song is. Kinda reminds me of 90s/early 2000s rock like Barenaked Ladies or They Might Be Giants. Huge fan of the Monotron Delay kicking in for flavor as well

There's a little TMBG buried somewhere in my DNA for sure and it rears its head from time to time.  I thought the Monotron Delay added a nice little something something to this as well.  Thanks for listening!



Tone Matrix wrote:

woot! those guitars get the fun groove going right away.  Catchy vocal harmonies and love how it goes into the mellotronny section where it takes off with the distortion.  Well done!

Thanks!  I wanted this one to take us on a bit of a ride so I hit a few different sections.  I liked how they came together.



PeterM wrote:

Great inspiration for a song! Great guitars, and whatever that wobbly high pitched thing is at the end lol! Great work.

That's probably the Korg Monotron Delay.  It's the newest toy I got so I've gotta use it a little bit.  smile  It probably won't end up on every track I do, but it'll be good to grab when I need a quick cool weird noise.



mzunguko wrote:

oh you got me math, we don't explain anything anymore, the younger kids are soon to be left with, well that's what the AI Oracle said the answer, all must bend to its wisdom (because we don't have any anymore)

I tried dividing by zero today and the world didn't end!

I agree, we seem to be heading in the direction of not retaining any knowledge in our own heads and instead relying on AI to tell us everything.  It's scary.



BarristerPlong wrote:

That fuzzed out acoustic was unexpected and put a huge smile on my face. Lyrics are amazing as always. This is really excellent.

Thank you.  I dig a fuzzed out acoustic sound and it'll probably crop up again at some point or another this year.



SQF wrote:

oh hell yeah this thing moves. Nice guitar work! Doubled vocals++++ 1:30 love the rhythmic lyric delivery. This is such a solid song!

Thanks!  I've been feeling the doubled vocals lately, so I'll probably keep doing them for a while.



TheGreyCat1026 wrote:

Absolutely love the bit at 2:41 omg

I like that part, too.  Thanks for listening!



RajaTheResidentAlien wrote:

EPIC vibes of INFINITE OMNIPOTENCE! It's as if, in thinking about how your math teacher said you "can't" do something, the spirit of the song is yelling out, "WE CAN DO ANYTHING!!" I love how you can take anything to this huge level of open-hearted positivity in your songs. I like the repeated lyrical motif at the end, too, taking it into a slightly different feel but still on the same level of 'YES I CAN!' while we roll out into the sunset heart

also, as for the math of 'dividing by zero', the word "can't" doesn't seem right since it was phrased like a 'rule', so i see your instinct is correct: if math is like science, these aren't 'rules' but more like 'descriptions/symbols' of 'nature'. my math teacher in elementary school didn't really phrase it like that(because i was in a classroom where we would've just kept asking "but why not?" if they did...) so i remember my math teacher specifically saying, "zero is the same as dividing by nothing, and if you divide by nothing, then it's as if you never divided anything, but instead multiplied it by infinity..." then they proceeded to show on a calculator how if you divide by numbers between 1 and 0, and get infinitessimally smaller, the result gets infinitely bigger (try dividing any number by 0.01 on a calculator, then try dividing that same number by 0.0000001 on the calculator, the result keeps getting larger)... which is interesting, when i hear your song here, the feel of it from beginning to end, gets infinitely bigger as we come to this point where you "divided by zero, now sit and watch the tears roll down", you come to that infinitely large feeling of an infinitely opened heart!! just saying, i see what ya did there wink heart

I like the way your math teachers explained it using a calculator to get closer and closer to zero and see what happens.  Of course, as the video Napear posted explains, it depends on which way you approach zero from if you approach positive or negative infinity, but I think that's a really good illustration of what's going on when you try to divide by zero.  Thanks for listening and for your insightful analysis of the track.  P.S. I really dug your track this week as well.





MRDRCAT wrote:

I love the sound and upbeat mood. My all-time favourite music genre is powerpop and I'd classify this not only as part of that genre but a solid representation that I will absolutely add to my summer playlist.


MRDRCAT wrote:

Side note: I appreciate the Monotron love

I think this could probably pass as powerpop for sure.  And the monotron is the newest toy I got, so I can't help but play with it a bit right now.  I'm impressed with what it can do.  I will definitely be sprinkling it in to more songs this year.

geopet wrote:

I can hear the smile on your face as you were singing the lyrics to this song. What a blast! Loved what you did with the doubling there, too. Everything just works in this song! Thank you for producing it. heart

It was mostly a joy to work on this one.  And thank YOU for listening.  smile



ineff wrote:

A new spin on "math rock" tongue  Your vocals on this track remind me of The Shins!

Napear wrote:

As a hardcore math nerd...


This was a great discussion, thanks!

Napear wrote:

There are plenty of algebras where you can/could divide by zero, they just aren't useful to humans doin' normal human things


There are... plenty of algebras?  (For non-humans?  Or possibly humans doing non-normal human things?)


I suppose this could technically qualify as math rock.  smile  I don't think I've gotten a vocal comparison to the Shins before, but I can hear what you're saying.  And yeah, I've enjoyed the discussion this track has prompted as well!


electronic_tiger wrote:

A strong turn of the millennium punk-rock-pop vibe that I haven't heard in a minute. Fun though! The synth/self-oscillating delay towards the end is wild. Cool little tune!

It's fun to hear the various things this track has reminded people of.  Turn of the millennium punk-rock-pop is a new comparison for me, but I believe it probably fits.  It was fun to get a little wild with the end of the track for sure.  Thanks for listening!



sleepside wrote:

Another sweet bit of power-pop, with a bright melody and vocal harmonies yes, but also some cool weirdness. Love the sneaky 6 -> 4 transitions from the mellotron-y sections to the main song. The peaky monotron sweep transitions are wild. And I love the tone in the guitar solo. Go! (go go go go go go go...)

I can't seem to help but inject a little bit of weirdness in.  Just makes things a little more interesting to me.  Thanks for listening and Go!  (go go go go go go go...)  smile



Chrisfoo wrote:

I was thinking Built to Spill right when I saw the title too like @jwh

This is great, the guitar is so crunchy and the sweepy lead thing is sweet. Love the bridge at 2:40 too, nice contrast.

I think the title alone will create that association, but I listened to that Built to Spill album a fair bit back in the day.  I'm sure it's seeped its way into my consciousness.



miraclemiles wrote:

Hey, great song. Vocals sounds great, love the lyrics. Acoustic sounds perfect for it. Came for the song, stayed for the math talk. It is interesting stuff that dividing by zero. I'm not sure I fully get it, and not sure I'll put my brain energy there now. Will probably check out the video Napear shared though. Smarter every day. Good song!

It's always nice when you get a good discussion or learn something while also making a track.  That video Napear posted actually does a really good job of explaining it and is worth watching for sure.



DESLRV wrote:

Good energy in this bop.
I think you've been told enough why you can't, it depends on the field really.
- Leega

A good energy bop for sure.  Thanks for listening!



lulub4ts wrote:

Went back to high school maths class with this one! Such a great bop, gonna be in my head all week. Kinda' gave me cosy but thoughtful TMBG vibes, which I what I used to listen to when I was meant to be doing maths homework

TMBG was a high school favorite of mine and they've undoubtedly wormed their way into my musical DNA.  This also does seem like the sort of subject matter they might tackle.  Thanks for listening!



emily wrote:

heart

I don't know why, but the grainy quality of this gif makes me happy.  It reminds me of watching Sesame Street or the Electric Company or something.

ohhh, I like that fuzz that kicks in!  Lots of cool guitar parts here.

More of that please. smile
Dig those Monotron Delay bursts too.  Do I hear mellotron too?  I've got a sweet spot for those.

rdomain wrote:

ohhh, I like that fuzz that kicks in!  Lots of cool guitar parts here.

More of that please. smile
Dig those Monotron Delay bursts too.  Do I hear mellotron too?  I've got a sweet spot for those.

Thanks!  I was happy with the guitar work on this one.  I'll definitely have to try to keep it up.  The Monotron Delay is great for adding little bits of texture.  I piled about four different synth sounds together for that mellotron section.  At least one of them may have been modeled after the mellotron (I don't remember off the top of my head what all I used), but the combined effect definitely comes across very mellotron-ish. 

You can be proud of this track. It has so many great elements. I had millions of goosebumps.

Q-Rosh wrote:

You can be proud of this track. It has so many great elements. I had millions of goosebumps.

Thanks!  This is one of my favorites of the year so far for sure.

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